Question

5 moles of liquid X and 10 moles of liquid Y make a solution having a vapor pressure of 70 torr. The vapor pressures of pure X and Y are 63 torr and 78 torr, respectively. Which of the following is true regarding the described solution?

• A. The solution shows negative deviation.
• B. The solution is ideal.
• C. The solution has volume greater than the sum of individual volumes.
• D. The solution shows positive deviation.

Hint:

A solution exhibits negative deviation when its vapor pressure is lower than expected based on Raoult's law. This occurs when the intermolecular forces between the components of the solution are stronger than between the components and the solvent.

Answer 1

The Correct Option is A

The vapor pressure of an ideal solution can be predicted using Raoult's law, which states: \[ P_{\text{solution}} = X_X P_X^0 + X_Y P_Y^0 \] Where: - \( P_{\text{solution}} \) is the vapor pressure of the solution, - \( X_X \) and \( X_Y \) are the mole fractions of X and Y, respectively, - \( P_X^0 \) and \( P_Y^0 \) are the vapor pressures of pure X and Y, respectively. Given: - Moles of X = 5, Moles of Y = 10, - \( P_X^0 = 63 \, \text{torr}, P_Y^0 = 78 \, \text{torr} \), - Total moles = 5 + 10 = 15. The mole fractions are: \[ X_X = \frac{5}{15} = \frac{1}{3}, \quad X_Y = \frac{10}{15} = \frac{2}{3} \] Now, applying Raoult's law: \[ P_{\text{solution}} = \left(\frac{1}{3}\right)(63) + \left(\frac{2}{3}\right)(78) \] \[ P_{\text{solution}} = 21 + 52 = 73 \, \text{torr} \] The given vapor pressure is 70 torr, which is lower than the calculated vapor pressure of 73 torr. This means the solution exhibits negative deviation from Raoult's law.
Thus, the solution shows negative deviation.
Therefore, the correct answer is (1) The solution shows negative deviation.